{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 07\n",
    "\n",
    "# 三维空间两点之间距离\n",
    "Book_3《数学要素》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1fda5eb-a001-458a-8ee8-95d0b90927b2",
   "metadata": {},
   "source": [
    "这段代码通过Matplotlib在三维空间中绘制了两个点$A$和$B$，并连接它们形成一条线段，以展示三维空间中的点与点之间的几何关系。具体步骤如下：\n",
    "\n",
    "1. **定义点$A$和点$B$的坐标**：点$A$的坐标为$(-2, 3, 1)$，点$B$的坐标为$(3, -1, -3)$，其中$x, y, z$分别代表每个点在三维空间中的位置。点$A$和点$B$的空间向量可以记作：\n",
    "   $$\n",
    "   \\vec{A} = (-2, 3, 1)\n",
    "   $$\n",
    "   $$\n",
    "   \\vec{B} = (3, -1, -3)\n",
    "   $$\n",
    "\n",
    "2. **计算线段的方向向量**：两点连成的线段的方向向量由$\\vec{B} - \\vec{A}$给出，其公式为：\n",
    "   $$\n",
    "   \\vec{AB} = (x_B - x_A, y_B - y_A, z_B - z_A) = (3 - (-2), -1 - 3, -3 - 1) = (5, -4, -4)\n",
    "   $$\n",
    "   该方向向量$\\vec{AB}$描述了从点$A$到点$B$的方向。\n",
    "\n",
    "3. **计算线段的长度**：线段$AB$的长度由向量$\\vec{AB}$的模（长度）给出：\n",
    "   $$\n",
    "   |\\vec{AB}| = \\sqrt{(x_B - x_A)^2 + (y_B - y_A)^2 + (z_B - z_A)^2} = \\sqrt{5^2 + (-4)^2 + (-4)^2} = \\sqrt{25 + 16 + 16} = \\sqrt{57}\n",
    "   $$\n",
    "   这个长度描述了点$A$与点$B$在三维空间中的欧几里得距离。\n",
    "\n",
    "4. **三维可视化**：在图形中，点$A$和点$B$被绘制成标记点，并用一条线段连接它们，形成直观的空间连接。代码采用正交投影（`ortho`），保证在三维视角下没有透视变形，使得各轴保持真实比例。此外，设置了坐标轴的范围为$[-4, 4]$，并添加浅灰色网格辅助观察。\n",
    "\n",
    "5. **视角调整**：代码将视角设置为方位角$-135$度和仰角$30$度，从这一角度可以清晰观察到点$A$、点$B$以及它们的连线在三维坐标系中的位置和结构。\n",
    "\n",
    "通过这些步骤，图形展示了点$A$和点$B$之间的距离和空间关系，是空间几何中点与点的连接、方向向量和距离计算的可视化呈现。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4ff0d30-eb9b-4ad5-ba18-bd6159e2f011",
   "metadata": {},
   "source": [
    "## 导入所需库"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "776a839e-c200-45b8-b1b1-eeaa9e822ab8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np  # 导入numpy库，用于数值计算\n",
    "import matplotlib.pyplot as plt  # 导入matplotlib库，用于绘图"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d55571e9-0600-4d98-a751-a0e0f5367a20",
   "metadata": {},
   "source": [
    "## 定义三维空间中的点A和点B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7b64dbfb-0cb9-4a72-b331-5fd8eb8670df",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_A = -2  # 点A的x坐标\n",
    "y_A = 3   # 点A的y坐标\n",
    "z_A = 1   # 点A的z坐标\n",
    "\n",
    "x_B = 3   # 点B的x坐标\n",
    "y_B = -1  # 点B的y坐标\n",
    "z_B = -3  # 点B的z坐标"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa6843ba-6074-4fd7-9fa6-1bc46310d1ef",
   "metadata": {},
   "source": [
    "## 创建图形"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0bd651d6-64ee-41ca-9a6a-bdd43d267bdd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()  # 创建图形对象\n",
    "ax = plt.axes(projection='3d')  # 创建三维坐标轴对象\n",
    "ax.plot([x_A, x_B], [y_A, y_B], [z_A, z_B], 'x', linestyle='-')  # 绘制点A和点B，并连接两点的线段\n",
    "\n",
    "ax.set_proj_type('ortho')  # 设置投影类型为正交投影\n",
    "\n",
    "## 设置坐标轴范围和标签\n",
    "ax.set_xlim(-4, 4)  # 设置x轴的显示范围为-4到4\n",
    "ax.set_ylim(-4, 4)  # 设置y轴的显示范围为-4到4\n",
    "ax.set_zlim(-4, 4)  # 设置z轴的显示范围为-4到4\n",
    "\n",
    "plt.tight_layout()  # 自动调整布局\n",
    "ax.set_xlabel(r'$\\it{x}$')  # 设置x轴标签\n",
    "ax.set_ylabel(r'$\\it{y}$')  # 设置y轴标签\n",
    "ax.set_zlabel(r'$\\it{z}$')  # 设置z轴标签\n",
    "\n",
    "## 设置视角和网格样式\n",
    "ax.view_init(azim=-135, elev=30)  # 设置视角，方位角为-135度，仰角为30度\n",
    "ax.xaxis._axinfo[\"grid\"].update({\"linewidth\":0.25, \"linestyle\" : \":\"})  # 设置x轴网格线样式\n",
    "ax.yaxis._axinfo[\"grid\"].update({\"linewidth\":0.25, \"linestyle\" : \":\"})  # 设置y轴网格线样式\n",
    "ax.zaxis._axinfo[\"grid\"].update({\"linewidth\":0.25, \"linestyle\" : \":\"})  # 设置z轴网格线样式"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
